Question

A small store keeps track of the number *X* of customers
that make a purchase during the first hour that the store is open
each day. Based on the records, *X* has the following
probability distribution.

X |
0 | 1 | 2 | 3 | 4 |

P(X) |
0.1 | 0.1 | 0.1 | 0.6 |

Determine P(x=2):

Determine P(x≥3):

Determine P(x<3):

Determine the mean number of customers:

Determine the standard deviation of the number of customers

Answer #1

Solution :

The sum of the probability is equal to 1 .

P(X) = 1

(a)

P(x = 2) = 1 - 0.1 - 0.1 - 0.1 - 0.6 = 0.1

(b)

P(x 3) = P(x = 3) + P(x = 4) = 0.1 + 0.6 = 0.7

(c)

P(x < 3) = P(x = 0) + P(x = 1) + P(x = 2) = 0.1 + 0.1 + 0.1 = 0.3

(d)

x | P(x) | x * P(x) |
x^{2} * P(x) |

0 | 0.1 | 0 | 0 |

1 | 0.1 | 0.1 | 0.1 |

2 | 0.1 | 0.2 | 0.4 |

3 | 0.1 | 0.3 | 0.9 |

4 | 0.6 | 2.4 | 9.6 |

Sum | 1 | 3 | 11 |

Mean = = X * P(X) = 3

(e)

Standard deviation =

=X
^{2} * P(X) -
^{2}

= 11
- 3^{2}

= 1.4142

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